Question

If the factors of a polynomial are (x-5) and (x²), what values of x make that polynomial 0?

Answer 1

The values of x that make the polynomial with factors (x-5) and (x²) equal to 0 are x = 5 and x = 0. The factor (x-5) equals zero when x is 5, and the factor (x²) equals zero when x is 0.

Step-by-step explanation:

If the factors of a polynomial are (x-5) and (x²), the values of x that make the polynomial 0 are x = 5 and x = 0. Here's why:

• For the factor (x-5), the value that makes it zero is x = 5 because if we substitute 5 for x, we get (5-5) which equals 0.
• For the factor (x²), the value that makes it zero is x = 0 because 0 squared (0²) is 0.

Each of these factors equate to zero at these specific values of x, satisfying the condition that a product of factors equals zero if and only if at least one of the factors is zero.